Preliminaries on Primes

17/9/2010

The one-million dollar question is: is there a definite order in the primes (2, 3, 5, 7, 11, 13 etc.) or are they essentially random? The one million dollars are waiting at the Clay Mathematical Institute in America for the one who solves the Riemann Hypothesis.

The great mathematician Gauss in the 19th century thought the primes were just randomly placed, but another mathematical genius of the time, Riemann, thought he had found the order of the primes. I quote from de Sautoy’s ‘Music of the Primes’: “Armed with a formula he kept secret from the world, Riemann discovered that whereas primes appeared chaotic, the points in his map were full of order. Instead of being randomly dotted around they were lining up in a straight line.”

To begin with we should pay special attention to the formulation of de Sautoy, because it generalises the big question, especially, ‘appeared chaotic’, ‘were full of order’ and the ‘lining up in a straight line’. I say this because I know I cannot solve the Riemann Hypothesis and therefore the million dollars will never be mine whatever solution I come up with, but I also know I have found what I think can be called a definite order in the primes and that is already years ago.

At the time, 2004, I sent the solution to Nature and received a standard rejection, subsequently, I sent it to the CWI (Centrum Wiskunde & Informatica) in Holland, where everybody was on holiday except a young mr. Batenburg who told me it was the second theorem of Fermat I had found and that computers could not factorize numbers of over a 140 digits. It was not interesting, he said.

My obsession with primes had started instantly with the discovery of my rational decimal nine-number system, inspired by Sumerian cuneiform clay tablets in 1998, on which the main whole-number-logic, or natural-number-logic, I present on this website, is based.

My first attempt at solving the riddle of the primes, together with the patterns of standing waves and masses of the solar system and the secrets of the Great Pyramid (mostly already published on this website), I sent as “A Theory of Resonance – (primes, planets, pyramids)” in 2003 to QI Ltd, Oxford, who produce the popular television program QI on the BBC for years now, and I was invited to their office in Turl street.
This is how I made acquaintance with John Lloyd and John Mitchinson, directors of QI, to whom I sent almost a year later the same, much shorter, copy on the primes I would sent to Nature. They did not feel qualified to judge it, understandably, nevertheless Mitchinson gave the impression that he saw the logic of it and, like me, was puzzled by the answer from CWI about computers.

I had been quite pleased, of course, to hear I had found the second theorem of Fermat as a total ignoramus and out of the blue, but I did not understand the reasoning of Batenburg about computers because the question is not what computers can do, but whether the logic of the solution stands.
I moved on and forgot about it, resigned to the idea that official science would not look into it, because the presentation was not professional and the solution embarrassingly simple.

Just a couple of weeks ago I was reminded of my solution by a newspaper story of a young mathematical prodigy enlisting at the university of Cambridge at 15, who has set himself the task of solving the Riemann Hypothesis. So I thought I give it another try, but now in my own setting.

If there is someone to solve the prime problem, it is most probably someone fresh, someone who is not yet totally conditioned by the things s/he has learned and been taught over the years and without which s/he cannot reason anymore, the general, so called ‘rational’, state of mind of scientists, which becomes incapable of considering anything that cannot be measured, like water divining for instance, without which people would not have survived in most places.

I think I find all these interesting things because I don’t have so many preconceived ideas; I may have un-learned what I was taught by others and learned to use my intuition.

I promise that I will soon give my solution to the order of the primes on this website and in such a way that the readers can check for themselves whether my arguments hold water. My readership will be my witness because Big Science will ignore me anyhow; it is good to share it after all these years.

My solution will not take the form of a professional presentation, but of the informal straightforward logic I use and which the reader can follow, I hope.
The solution is a transparent net which necessarily catches all the primes without exception and which shows their order and intricate relations.
It is again a joy to see the simplicity and beauty of the solution.
It is the beauty of this model which has kept me going for all these years, since: ‘Beauty is Truth’, especially in mathematics.

The lists of primes I use to show the logic can be found on Internet. The solution is based on the decimal system and therefore has no universal value for mathematicians, probably, but no doubt it can be turned round by one of them into a more sophisticated formula, which is more like the Riemann Hypothesis (zeros at sea level!?) and s/he will take the prize. Well, let them have it.

In the end the crucial question is whether primes show definite order, whether in a decimal system or not. The question is not whether Riemann’s Hypothesis is right, although that may be the most mathematically elegant and deep solution, but it might be wrong as well; the fact remains that it has not been solved in one and a half century now.
My solution is based on simple logic where the numbers themselves show the way, again.

The point maybe that my solution comes from a field that mathematicians call : ‘recreational mathematics’, that is a field for amateurs where most mathematicians are not interested in because it is too simple-minded; a bit like the mathematical model this site is about, it is too simple and outside their routine way of thinking to be taken seriously, they refuse to spend time studying it and to appreciate its logic.
Without a peer review it does not exist in science, nor for the Clay Institute.
Unfortunately I have no peers in these matters.

So let the professionals grope in the dark for another century before they find their solution, if they do, while my readers will know that there is an answer they can understand, whereas they, like me, will never understand the Riemann Hypothesis anyway.
My solution is basically simple and understandable for anybody and the answer is not necessarily in Riemann’s zeros, but in rows of other numbers, the answer is of a simplicity which mathematicians, no doubt, will deem too trivial to consider.
But the chickens will come home to roost, I think.

I have found so many incredible things with this simple number-logic (numero-logica?) so far, so why not the order of the primes, albeit in ‘recreational form’.

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